Reduction and duality in generalized geometry

TL;DR

This paper extends generalized geometry reduction techniques to Poisson Lie group actions, demonstrating the existence of generalized Kähler reduction under broader conditions and linking it to string theory T-duality with non-abelian groups.

Contribution

It introduces a new reduction construction for generalized Kähler structures under Poisson Lie group actions, even when only one structure is preserved, and connects this to string theory T-duality.

Findings

Generalized Kähler reduction exists with partial preservation of structures.

String theory T-duality with H-fluxes arises from such reductions.

Reductions can involve non-abelian groups.

Abstract

Extending our reduction construction in \cite{Hu} to the Hamiltonian action of a Poisson Lie group, we show that generalized K\"ahler reduction exists even when only one generalized complex structure in the pair is preserved by the group action. We show that the constructions in string theory of the (geometrical) $T$-duality with $H$-fluxes for principle bundles naturally arise as reductions of factorizable Poisson Lie group actions. In particular, the group may be non-abelian.